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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 24 Dec 2010 13:44:50 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t1293198249147djres3efxpg8.htm/, Retrieved Tue, 30 Apr 2024 06:33:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114955, Retrieved Tue, 30 Apr 2024 06:33:02 +0000

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Estimated Impact

122

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-       [(Partial) Autocorrelation Function] [autocorrelation D=1] [2010-12-24 13:44:50] [27f38de572a508a633f0ad2411de6a3e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114955&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114955&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.941674	6.5917	0
2	0.818349	5.7284	0
3	0.642704	4.4989	2.1e-05
4	0.449514	3.1466	0.001404
5	0.248719	1.741	0.043977
6	0.062191	0.4353	0.332616
7	-0.109465	-0.7663	0.223601
8	-0.267713	-1.874	0.03345
9	-0.411742	-2.8822	0.002924
10	-0.527338	-3.6914	0.00028
11	-0.603827	-4.2268	5.1e-05
12	-0.638831	-4.4718	2.3e-05
13	-0.611177	-4.2782	4.4e-05
14	-0.538141	-3.767	0.000222
15	-0.431516	-3.0206	0.002
16	-0.323094	-2.2617	0.014095
17	-0.210634	-1.4744	0.07338

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941674 & 6.5917 & 0 \tabularnewline
2 & 0.818349 & 5.7284 & 0 \tabularnewline
3 & 0.642704 & 4.4989 & 2.1e-05 \tabularnewline
4 & 0.449514 & 3.1466 & 0.001404 \tabularnewline
5 & 0.248719 & 1.741 & 0.043977 \tabularnewline
6 & 0.062191 & 0.4353 & 0.332616 \tabularnewline
7 & -0.109465 & -0.7663 & 0.223601 \tabularnewline
8 & -0.267713 & -1.874 & 0.03345 \tabularnewline
9 & -0.411742 & -2.8822 & 0.002924 \tabularnewline
10 & -0.527338 & -3.6914 & 0.00028 \tabularnewline
11 & -0.603827 & -4.2268 & 5.1e-05 \tabularnewline
12 & -0.638831 & -4.4718 & 2.3e-05 \tabularnewline
13 & -0.611177 & -4.2782 & 4.4e-05 \tabularnewline
14 & -0.538141 & -3.767 & 0.000222 \tabularnewline
15 & -0.431516 & -3.0206 & 0.002 \tabularnewline
16 & -0.323094 & -2.2617 & 0.014095 \tabularnewline
17 & -0.210634 & -1.4744 & 0.07338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114955&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.941674[/C][C]6.5917[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.818349[/C][C]5.7284[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.642704[/C][C]4.4989[/C][C]2.1e-05[/C][/ROW]
[ROW][C]4[/C][C]0.449514[/C][C]3.1466[/C][C]0.001404[/C][/ROW]
[ROW][C]5[/C][C]0.248719[/C][C]1.741[/C][C]0.043977[/C][/ROW]
[ROW][C]6[/C][C]0.062191[/C][C]0.4353[/C][C]0.332616[/C][/ROW]
[ROW][C]7[/C][C]-0.109465[/C][C]-0.7663[/C][C]0.223601[/C][/ROW]
[ROW][C]8[/C][C]-0.267713[/C][C]-1.874[/C][C]0.03345[/C][/ROW]
[ROW][C]9[/C][C]-0.411742[/C][C]-2.8822[/C][C]0.002924[/C][/ROW]
[ROW][C]10[/C][C]-0.527338[/C][C]-3.6914[/C][C]0.00028[/C][/ROW]
[ROW][C]11[/C][C]-0.603827[/C][C]-4.2268[/C][C]5.1e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.638831[/C][C]-4.4718[/C][C]2.3e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.611177[/C][C]-4.2782[/C][C]4.4e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.538141[/C][C]-3.767[/C][C]0.000222[/C][/ROW]
[ROW][C]15[/C][C]-0.431516[/C][C]-3.0206[/C][C]0.002[/C][/ROW]
[ROW][C]16[/C][C]-0.323094[/C][C]-2.2617[/C][C]0.014095[/C][/ROW]
[ROW][C]17[/C][C]-0.210634[/C][C]-1.4744[/C][C]0.07338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114955&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.941674	6.5917	0
2	0.818349	5.7284	0
3	0.642704	4.4989	2.1e-05
4	0.449514	3.1466	0.001404
5	0.248719	1.741	0.043977
6	0.062191	0.4353	0.332616
7	-0.109465	-0.7663	0.223601
8	-0.267713	-1.874	0.03345
9	-0.411742	-2.8822	0.002924
10	-0.527338	-3.6914	0.00028
11	-0.603827	-4.2268	5.1e-05
12	-0.638831	-4.4718	2.3e-05
13	-0.611177	-4.2782	4.4e-05
14	-0.538141	-3.767	0.000222
15	-0.431516	-3.0206	0.002
16	-0.323094	-2.2617	0.014095
17	-0.210634	-1.4744	0.07338

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.941674	6.5917	0
2	-0.603979	-4.2279	5.1e-05
3	-0.34195	-2.3937	0.010278
4	0.080251	0.5618	0.288422
5	-0.12871	-0.901	0.186006
6	-0.008302	-0.0581	0.476946
7	-0.14304	-1.0013	0.160806
8	-0.267431	-1.872	0.03359
9	-0.13225	-0.9257	0.179557
10	0.069179	0.4843	0.315182
11	0.065582	0.4591	0.324107
12	-0.084606	-0.5922	0.278206
13	0.306085	2.1426	0.01857
14	-0.137047	-0.9593	0.171052
15	-0.164893	-1.1543	0.126998
16	-0.180655	-1.2646	0.106002
17	0.09198	0.6439	0.261334

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941674 & 6.5917 & 0 \tabularnewline
2 & -0.603979 & -4.2279 & 5.1e-05 \tabularnewline
3 & -0.34195 & -2.3937 & 0.010278 \tabularnewline
4 & 0.080251 & 0.5618 & 0.288422 \tabularnewline
5 & -0.12871 & -0.901 & 0.186006 \tabularnewline
6 & -0.008302 & -0.0581 & 0.476946 \tabularnewline
7 & -0.14304 & -1.0013 & 0.160806 \tabularnewline
8 & -0.267431 & -1.872 & 0.03359 \tabularnewline
9 & -0.13225 & -0.9257 & 0.179557 \tabularnewline
10 & 0.069179 & 0.4843 & 0.315182 \tabularnewline
11 & 0.065582 & 0.4591 & 0.324107 \tabularnewline
12 & -0.084606 & -0.5922 & 0.278206 \tabularnewline
13 & 0.306085 & 2.1426 & 0.01857 \tabularnewline
14 & -0.137047 & -0.9593 & 0.171052 \tabularnewline
15 & -0.164893 & -1.1543 & 0.126998 \tabularnewline
16 & -0.180655 & -1.2646 & 0.106002 \tabularnewline
17 & 0.09198 & 0.6439 & 0.261334 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114955&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.941674[/C][C]6.5917[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.603979[/C][C]-4.2279[/C][C]5.1e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.34195[/C][C]-2.3937[/C][C]0.010278[/C][/ROW]
[ROW][C]4[/C][C]0.080251[/C][C]0.5618[/C][C]0.288422[/C][/ROW]
[ROW][C]5[/C][C]-0.12871[/C][C]-0.901[/C][C]0.186006[/C][/ROW]
[ROW][C]6[/C][C]-0.008302[/C][C]-0.0581[/C][C]0.476946[/C][/ROW]
[ROW][C]7[/C][C]-0.14304[/C][C]-1.0013[/C][C]0.160806[/C][/ROW]
[ROW][C]8[/C][C]-0.267431[/C][C]-1.872[/C][C]0.03359[/C][/ROW]
[ROW][C]9[/C][C]-0.13225[/C][C]-0.9257[/C][C]0.179557[/C][/ROW]
[ROW][C]10[/C][C]0.069179[/C][C]0.4843[/C][C]0.315182[/C][/ROW]
[ROW][C]11[/C][C]0.065582[/C][C]0.4591[/C][C]0.324107[/C][/ROW]
[ROW][C]12[/C][C]-0.084606[/C][C]-0.5922[/C][C]0.278206[/C][/ROW]
[ROW][C]13[/C][C]0.306085[/C][C]2.1426[/C][C]0.01857[/C][/ROW]
[ROW][C]14[/C][C]-0.137047[/C][C]-0.9593[/C][C]0.171052[/C][/ROW]
[ROW][C]15[/C][C]-0.164893[/C][C]-1.1543[/C][C]0.126998[/C][/ROW]
[ROW][C]16[/C][C]-0.180655[/C][C]-1.2646[/C][C]0.106002[/C][/ROW]
[ROW][C]17[/C][C]0.09198[/C][C]0.6439[/C][C]0.261334[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114955&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.941674	6.5917	0
2	-0.603979	-4.2279	5.1e-05
3	-0.34195	-2.3937	0.010278
4	0.080251	0.5618	0.288422
5	-0.12871	-0.901	0.186006
6	-0.008302	-0.0581	0.476946
7	-0.14304	-1.0013	0.160806
8	-0.267431	-1.872	0.03359
9	-0.13225	-0.9257	0.179557
10	0.069179	0.4843	0.315182
11	0.065582	0.4591	0.324107
12	-0.084606	-0.5922	0.278206
13	0.306085	2.1426	0.01857
14	-0.137047	-0.9593	0.171052
15	-0.164893	-1.1543	0.126998
16	-0.180655	-1.2646	0.106002
17	0.09198	0.6439	0.261334

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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